William M. Briggs

Statistician to the Stars!

Page 395 of 416

It was bound to happen

Remember how you used to cavalierly ignore those “Keep of the Grass Signs” in your un-enlightened youth?

Well, you brutal, uncaring, beast.

For it has finally been announced—from Europe, naturally, from the Swiss government-appointed Federal Ethics Committee on Non-Human Biotechnology—that plants have feelings too.

They have authoritatively stated that “interfering with plants without a valid reason as ‘morally inadmissible.’” This means the next time you carve you and your sweetheart’s name into a tree can lead to a nice, long jail sentence. (If the famed Swiss police ever catch you, that is.)

The ethics committee did grudgingly admit—for now—that “all action involving plants for the preservation of the human race was morally justified.” Meaning, I suppose, that it’s still OK to eat them. I probably don’t need to explain to you the fix we’d be in if we could not. But there is only direction for the Enlightened to go, so stay tuned for an announcement banning the use of “higher” plants, such as maybe corn and tomatoes, for use in the “preservation of the human race.”

The august Swiss body has also found that “genetic modification of a plant did not contradict the idea of its ‘dignity’.” Yes, I can see how a kumquat would not find it an affront to be genetically probed. Until, that is, the kumquat learns how easily this sort of thing can sully one’s reputation. It’s only matter of time before a lawyer figures this out and brings a case to Brussels.

Just keep all this in mind, think about what you are doing—raise your awareness!—next time you are at the salad bar.

The Devil’s Delusion: Atheism and its Scientific Pretensions by David Berlinski

There are, as everybody knows, a recent number of books seeking to either demonstrate, scientifically, that God does not exist, or to show that the love of religion is the root of all evil. Some familiar names: Daniel Dennet, Richard Dawkins, Stephen Weinberg, Victor Stenger, Christopher Hitchens, and even John Allen Paulos. All proclaim that the weight of scientific evidence is either completely or heavily on the side of the non existence of God.

The question is, of course: Has the authority of eminent scientists enabled them to prove their case? Berlinski says, “Not even close.” Not only have they not come close, Berlinski goes further and shows how easily they are persuaded by weak or demonstrably false arguments, and the extraordinary lengths that some scientists will go, in the sense of believing bizarre theories, to avoid ceding any ground to the “religionists.” Their distaste of religion has also lead them to say some rather stupid things. For example, Berlinski quotes the eminent biologist Emile Zuckerkandl as saying that if God exists, He would represent “something like a pathology of the state of being.” An enjoyable, sputtering rant by that author published in the peer-reviewed journal Gene is summarized later in the book.

Incidentally, before we get too far, it is worth mentioning that like most (all?) books in this genre, Berlinski does not attempt a definition of who or what God is—and neither do those on the other side. I haven’t one to offer, either. This curiosity can very well mean that everybody is talking at cross purposes. But since nobody delineates or bounds God, I can’t say much more than this, except that it should be borne in mind when reading any of these books.

A non-Enlightened disease

Berlinski puts the claim that religion is bad for you in perspective. Some anti-religion authors won’t settle for anything less than damning religion in all its stripes, disallowing, even, the crumb of comfort given to people when their loved ones die. Even Carl Sagan, in his Demon-Haunted World allowed this kind of solace, without recognizing that since, I must point out, everybody dies, this is an enormous amount of comfort to go around that would be denied mankind if religion were absent. But you never hear of our authors breaking open Mill to assist in calculating the utility of comforts versus torments of religion.

Many scientists feel that religion, while still a cancerous growth, is benign and only mostly harmful, and not immediately deadly. Sort of like smoking, which the more Enlightened among us would like to ban. Presumably, those who would prohibit smoking are same people who would support legalizing assisted suicide. Which happened in Holland in 1984 (and where a partial smoking ban does exist). Since then, about three percent of all deaths in that country are assisted, of which the government admits that about one-fourth are “involuntary.” We call that involuntary method of exiting “murder” here in the States, but Europeans are often considered more Enlightened, so they might be one step ahead of us in legal definitions.

Arguments for assisted suicide are usually intentionally religion-free. Thus, the point of the Holland example, of course, is that the world would not necessarily become a more moral, or safer place, if religion were to disappear. More proof is given by Berlinski in the form of a table, ordered by number of “excess”, or untimely, twentieth-century deaths due to non- or even anti-religious behavior. Leading the pack are of course the two World Wars, but not far behind in the body count are mankind’s experiments with various communist utopias. Since one of the top arguments used by those who would wish to bar religion is that the religious can be cruel and have killed, the evidence that the non-religious can be cruel and have killed in equal or larger number only proves that there will always be a class of people who adore pain, misery, and bloodshed, irrespective of creed.

The disease religion is also seen as congenital, in the sense that people have religion on the brain, literally. Somehow, we are assured, the brain has genetically encoded religion into itself, and that if we’d just grow up and recognize this, we would become Enlightened (or brightened, these days). This is one of the sillier arguments put forth by scientists. If religion is genetically encoded, then it cannot be overcome, unless some of us, the superior ones naturally, have somehow managed to escape expressing those particular genes that activate, say, the praying response. Look for one of those fMRI studies that “proves” this, soon.

Berlinski shows that because some scientists cannot countenance religious arguments of any kind, they refuse to accept any evidence that is any way tainted by religion. This leads to the fallacy that one should not listen to arguments against, say, stem cell research or abortion because they are religious. You will surely certainly recognize this ploy when you meet it.

Scientific ontology

Everybody already knows that physics, and its offshoots, has done brilliantly at explaining more and more of the universe. But it cannot keep doing so forever. At some point, meta-physics must enter into the discussion. This is because, no matter what physical laws we have identified, we will never have explained through observation why these particular laws and not some other are in force, nor can we answer what the laws mean. It is obvious that it is here that God can slip in and offer the needed explanations. Some scientists are therefore anxious to fill in these gap with…something, anything but God. Or, if that cannot be accomplished, then to prove that God does not exist.

Dawkins, in his The God Delusion offers a particularly weak argument. His first premise is that the universe is improbable. And we can stop right there, because that is a nonsensical statement, so his argument fails. Any thing or statement cannot be improbable. A thing can only be improbable with respect to something else. Further, a thing can be improbable with respect to one set of evidence and entirely probable with respect to other evidence. So, in Dawkin’s case, the universe is improbable with respect to what?

Weak Anthropic evidence is sometimes offered, in the guise of certain physical constants having particular values, in the sense that if these constants did not have these values, then human life would be impossible (which is not the same as saying the universe is impossible, but let that pass). Now the burden is on those who tout this evidence to show that this is the best evidence with which to measure the improbability of the universe. And there are many hints that it is not the best evidence. It is, after all, by its very name, suspiciously self indulgent and human centered evidence. Why would the universe care if humans, or other sentient beings, evolved enough to notice that they might not have evolved had the universe been arranged differently anyway? Besides, to say that things might have been different and humans might not have evolved is just a tautology, and therefore of no interest.

Still, accept it if you like, so that we can move to Dawkins’s second premise, which is that God Himself is improbable. Again, the statement is nonsensical: improbable with respect to what? Dawkins suggests that God must be more improbable than the universe, which again makes no sense. Anyway, improbable is not impossible, as Dawkins often argues with respect to evolution by natural selection, arguments he has apparently forgotten. Still, Dawkins moves to his conclusion that God is so improbable that He doesn’t exist, and advises people to accept some recent conjectures in cosmology that seem to do away with the need to explain why the universe, or universes, are the way they are.

These are the Landscape and multiverse hypotheses, put forward by various authors to help them cope with the insolubilities of quantum mechanics and cosmology. These are attempts to shift the questions of “Why?” one step back. That they do not answer them, I would have thought obvious. Even pushing the grand questions a little deeper down is enough to please some people. Berlinski, a mathematical physicist, covers these speculations well, without any math, and gives pointers to books where we might learn more. See especially his very clever “Catechism of Quantum Cosmology.” Briefly, however, the solutions offered posit an uncountable number of alternate universes that are coming into and out of creation always. There are no mechanisms to observe these other universes directly or indirectly. Even if we could, these theories might answer some questions of quantum mechanics and gravity, but they never answer why it is infinities of universes instead of just one. The theories are also mind-boggling complex, and by no means are they consistent with one another. Nobody even knows what the full scope of these ideas are.

Berlinski quotes Dawkins, who is nevertheless satisfied, as saying, “The key difference between the radically extravagant God hypothesis and the apparently extravagant multiverse hypothesis, is one of statistical improbability.” Presumably, he means that God is more improbable. He never says how much more. Infinities, of universes or anything else, are a dangerous thing. More foolishness has been generated by jumping to infinity than by any other reason (see chapter 15 of Jaynes’s remarkable Probability Theory for appropriate words of admonition).

Argument from design

It has long been convincing to many that the wonderful biological complexity that is everywhere in evidence must have had a designer. How else, Darwin himself wondered, can one explain the human eye? This argument is less convincing than it once was, because of the success of modern biology and genetics, and the seeming success of evolution by natural selection.

(It is just as well to point out here that I accept that evolution accounts for some or most of the observed biological variation on Earth, and that the mechanism driving it is natural selection, or something like it.)

Wait a minute. Did he just say seeming success? He did. Which brings us back to Dawkins, the best-known anti-religion author. Was there ever a man who published so much nonsense that was taken so seriously by the scientific community? Nobody else even comes close. Just mentioning the word memes proves my point. Is not believing in God a meme? Berlinski doesn’t discuss memes, but does offer some well known criticisms of “selfish” genes—incidentally, the best are due to the philosopher’s Mary Midgley (Evolution as a Religion) and David Stove (Darwinian Fairytales; if you haven’t read either of these books, please do so, especially Stove’s, before you comment).

Not all biologists are satisfied with present-day theory. Berlinski writes

[Darwinian] theory is what is always was: It is unpersuasive. Among evolutionary biologists, these matters are well known. In the privacy of the Susan B. Anthony faculty lounge, they often tell one another with relief that it is a very good thing the public has no idea what the research literature really suggest.

“Darwin?” a Nobel laureate in biology once remarked to me over his bifocals. “That’s just the party line.”

There are still gaps in the evolutionary record. Nobody knows how life original arose, and nobody knows how species originate. Some fill these gaps with God. Scientists argue that the gaps will be filled in eventually. Berlinski says that this assumption is “both intellectually primitive and morally abhorrent—primitive because it reflects a phlegmatic absence of curiosity, and abhorrent because it assigns to intellectual future a degree of authority alien to human experience” because filling gaps “has created [new] gaps all over again.”

The answer

The best summation on the side of (non-apoplectic) scientists is probably from Richard Feynman, who said, “Today we cannot see whether Schrödinger’s equation [which describes the time evolution of physical systems] contains frogs, musical composers, or morality. We cannot say whether something beyond it like God is needed , or not. And so we can all hold strong opinions either way.”

To say whether or not God exists is the hardest question in the world; yet it is the one people find easiest to answer, and everybody seems delighted to meet an argument, however weak, that agrees with their desires. This leads very smart people to say exceptionally stupid things.

My own surmise is that any proof—for or against—is impossible. And so any belief you have is based entirely on faith.

Why multiple climate model agreement is not that exciting

There are several global climate models (GCMs) produced by many different groups. There are a half dozen from the USA, some from the UK Met Office, a well known one from Australia, and so on. GCMs are a truly global effort. These GCMs are of course referenced by the IPCC, and each version is known to the creators of the other versions.

Much is made of the fact that these various GCMs show rough agreement with each other. People have the sense that, since so many “different” GCMs agree, we should have more confidence that what they say is true. Today I will discuss why this view is false. This is not an easy subject, so we will take it slowly.

Suppose first that you and I want to predict tomorrow’s high temperature in Central Park in New York City (this example naturally works for any thing we want to predict, from stock prices to number of people who will vote for a certain USA presidential candidate). I have a weather model called MMatt. I run this model on my computer and it predicts 66 degrees F. I then give you this model so that you can run it on your computer, but you are vain and rename the model to MMe. You make the change, run the model, and announce that MMe predicts 66 degrees F.

Are we now more confident that tomorrow’s high temperature will be 66 because two different models predicted that number?

Obviously not.

The reason is that changing the name does not change the model. Simply running the model twice, or a dozen, or a hundred times, does not give us any additional evidence than if we only ran it just once. We reach the same conclusion if instead of predicting tomorrow’s high temperature, we use GCMs to predict next year’s global mean temperature: no matter how many times we run the model, or how many different places in the world we run it, we are no more confident of the final prediction than if we only ran the model once.

So Point One of why multiple GCMs agreeing is not that exciting is that if all the different GCMs are really the same model but each just has a different name, then we have not gained new information by running the models many times. And we might suspect that if somebody keeps telling us that “all the models agree” to imply there is greater certainty, he either might not understand this simple point or he has ulterior motives.

Are all the many GMCs touted by the IPCC the same except for name? No. Since they are not, then we might hope to gain much new information from examining all of them. Unfortunately, they are not, and can not be, that different either. We cannot here go into detail of each component of each model (books are written on these subjects), but we can make some broad conclusions.

The atmosphere, like the ocean, is a fluid and it flows like one. The fundamental equations of motion that govern this flow are known. They cannot differ from model to model; or to state this positively, they will be the same in each model. On paper, anyway, because those equations have to be approximated in a computer, and there is not universal agreement, nor is there a proof, of the best way to do this. So the manner each GCM implements this approximation might be different, and these differences might cause the outputs to differ (though this is not guaranteed).

The equations describing the physics of a photon of sunlight interacting with our atmosphere are also known, but these interactions happen on a scale too small to model, so the effects of sunlight must be parameterized, which is a semi-statistical semi-physical guess of how the small scale effects accumulate to the large scale used in GCMs. Parameterization schemes can differ from model to model and these differences almost certainly will cause the outputs to differ.

And so on for the other components of the models. Already, then, it begins to look like there might be a lot of different information available from the many GCMs, so we would be right to make something of the cases where these models agree. Not quite.

The groups that build the GCMs do not work independently of one another (nor should they). They read and write for the same journals, attend the same conferences, and are familiar with each other’s work. In fact, many of the components used in the different GCMs are the same, even exactly the same, in more than one model. The same person or persons may be responsible, through some line of research, for a particular parameterization used in all the models. Computer code is shared. Thus, while there are some reasons for differing output (and we haven’t covered all of them yet), there are many more reasons that the output should agree.

Results from different GCMs are thus not independent, so our enthusiasm generated because they all roughly agree should at least be tempered, until we understand how dependent the models are.

This next part is tricky, so stay with me. The models differ in more ways than just the physical representations previously noted. They also differ in strictly computational ways and through different hypotheses of how, for example, CO2 should be treated. Some models use a coarse grid point representation of the earth and others use a finer grid: the first method generally attempts to do better with the physics but sacrifices resolution, the second method attempts to provide a finer look at the world, while typically sacrificing accuracy in other parts of the model. While the positive feedback in temperature caused by increasing CO2 is the same in spirit for all models, the exact way it is implemented in each can differ.

Now, each climate model, as a result of the many approximations that must be made, has, if you like, hundreds (even thousands) of knobs that can be dialed to and fro. Each twist of the dial produces a difference in the output. Tweaking these dials, then, is a necessary part of the model building process. The models are tuned so that they, as closely as possible, first are able to produce climate that looks like the past, already observed, climate. Much time is spent tuning and tweaking the models so that they can, at least roughly, reproduce past climate. Thus, the fact that all the GCMs can roughly represent the past climate is again not as interesting as it first seemed. They better had, or nobody would seriously consider the model as a contender.

Reproducing past data is a necessary but not sufficient condition that the models can predict future data. Thus, it is also not at all clear how these tweakings affect the accuracy in predicting new data, which is data that was not used in any way to build the models, that is, future data. Predicting future data has several components.

It might be that one of the models, say GCM1 is the best of the bunch in the sense that it matches most closely future data. If this is always the case, if GCM1 is always closest (using some proper measure of skill), then it means that the other models are not as good, they are wrong in some way, and thus they should be ignored when making predictions. The fact that they come close to GCM1 should not give us more reason to believe the predictions made by GCM1. The other models are not providing new information in this case. This argument, which is admittedly subtle, also holds if a certain group of GCMs are always better than the remainder of models. Only the close group can be considered independent evidence.

Even if you don’t follow—or believe—that argument, there is also the problem of how to quantify the certainty of the GCM predictions. I often see pictures like this:
GCM predictions
Each horizontal line represents the output of a GCM, say predicting next year’s average global temperature. It is often thought that the spread of the outputs can be used to describe a probability distribution over the possible future temperatures. The probability distribution is the black curve drawn over the predictions, and neatly captures the range of possibilities. This particular picture looks to say that there is about a 90% chance that the temperature will be between 10 and 14 degrees. It is at this point that people fool themselves, probably because the uncertainty in the forecast has become prettily quantified by some sophisticated statistical routines. But the probability estimate is just plain wrong.

How do I know this? Suppose that each of the eight GCMs predicted that the temperature will be 12 degrees. Would we then say, would anybody say, that we are now 100% certain in the prediction?

Again, obviously not. Nobody would believe that if all GCMs agreed exactly (or nearly so) that we would be 100% certain of the outcome. Why? Because everybody knows that these models are not perfect.

The exact same situation was met by meteorologists when they tried this trick with weather forecasts (this is called ensemble forecasting). They found two things. The probability forecasts made by this averaging process were far too sure—the probabilities, like our black curve, were too tight and had to made much wider. Second, the averages were usually biased—meaning that the individual forecasts should all be shifted upwards or downwards by some amount.

This should also be true for GCMs, but the fact has not yet been widely recognized. The amount of certainty we have in future predictions should be less, but we also have to consider the bias. Right now, all GCMs are predicting warmer temperatures than are actually occurring. That means the GCMs are wrong, or biased, or both. The GCM forecasts should be shifted lower, and our certainty in their predictions should be decreased.

All of this implies that we should take the agreement of GCMs far less seriously than is often supposed. And if anything, the fact that the GCMs routinely over-predict is positive evidence of something: that some of the suppositions of the models are wrong.

Spanish Expedition

I have returned from Madrid, where the conference went moderately well. My part was acceptable, but I could have done a better job, which I’ll explain in a moment.

Iberia Airlines is reasonable, but the seats in steerage were even smaller than I thought. On the way there, I sat next to a lady whose head kept lolling over onto me as she slept. The trip back was better, because I was able to commandeer two sets. Plus, there were a large, boisterous group of young Portuguese men who apparently had never been to New York City before. They were in high spirits for most of the trip, which made the journey seem shorter. About an hour before landing they started to practice some English phrases which they thought would be useful for picking up American women: “Would you go out with me?”, “I like you”, and “You are a fucking sweetheart.”

My talk was simultaneously translated in Spanish, and I wish I would have been more coherent and that I would have talked slower. The translator told me afterwards that I talked “rather fast.” I know I left a lot of people wondering.

The audience was mostly scientists (of all kinds) and journalists. My subject was rather technical and new, and while I do think it is a useful approach, it is not the best talk to present to non-specialists. My biggest fault was my failure to recognize and speak about the evidence that others found convincing. I could have offered a more reasonable comparison if I had done so.

I’ll write about these topics in more depth later, but briefly: people weight heavily the fact that many different climate models are in agreement in closely simulating past observations. There are two main, and very simple problems with this evidence, which I could have, at the time, done a better job pointing out. For example, I could have asked this question: why are there any differences between climate models? The point being that eight climate models agreeing is not eight independent pieces of evidence. All of these models, for instance, use the same equations of motion. We should be surprised that there are any differences between them.

The second problem I did point out, but I do not think I was convincing. So far, climate models over-predict independent data: that is, they all forecast higher temperatures than are actually observed. This is for data that was not used to fit the models. This means, this can only mean, that the climate models are wrong. They might not be very wrong, but they are wrong just the same. So we should be asking: why are they wrong?

There was a press conference, conducted in Spanish. I can read Spanish much better than I can hear it, which is a fault I should work harder to correct, but it meant that I could not follow most of the comments or questions well. I was the critical representative, and a Professor Moreno was my foil. The most pertinent question to me was (something like) “Do I think it is time for new laws to be passed to combat global warming?” I said no. Professor Moreno vehemently disagreed, incorrectly using as an example the unfortunate heat wave in Spain that was responsible for a large number of deaths. Incorrect, because it is impossible to say that this particular heat wave was caused by humans (in the form of anthropogenic global warming). But the press there, like here (like everywhere), enjoyed the conflict between us, so this is what was reported.

Here, for the sake of vanity, are some links (in Spanish) for the news coverage. We were also on the Spanish national television news on the first night of the conference, but I didn’t see it because we were out. Some of these links may, of course, expire.

  1. ?Existe el cambio clim?tico?
  2. Estad?stico de EEUU rebaja la fiabilidad de las predicciones del IPCC contra la opini?n general
  3. Un estad?stico americano pone en duda la veracidad del cambio clim?tico
  4. Un experto americano duda de las consecuencias del cambio clim?tico
  5. Evidencias apabullantes
  6. Un debate sobre cambio clim?tico termina a gritos en Madrid

Madrid itself was wonderful, and my hosts Francisco Garc?a Novo y Antonio Cembrero were absolute gentlemen, and I met many lovely people. I was introduced to several excellent restaurants and cervesaria. The food was better than I can write about—I nearly wept at the Museo del Jamon. I felt thoroughly spoiled. Dr Novo introduced me to La Grita, a subtle sherry that is a perfect foil for olives. I managed to find some in the duty free shop, and I recommend that if you see some, snatch it up.

Come back over the next few days. By then, I hope to have written something on the agreement of climate models.

Tall men in planes

I am off to Spain today, for the conference, to present my unfinished, and unfinishable, talk. Why unfinishable? I am asking people to supply estimates for certain probabilities (see the previous post), on which there will never be agreement, nor will these estimates cease changing through time. I am somewhat disheartened by this, and would like to say something more concrete, but I am committed. So. It’s eight hours there and back, crammed into a seat made for, let us say, those of a more diminutive stature than I. There will be no more postings until Saturday, when I return, which is why I leave you with this classic column I wrote several years ago, but which is just as relevant today.

Burden of the very tall

Lamentations of the Very Tall

An alternate title of this article could have been, “Short People Rejoice!” for it’s my conviction that the world is mercilessly biased in favor of tiny people. That is, probably you.

I say “probably you” because of the firm statistical grounding in the fact that it is quantifiably improbable for a random person to be tall. I’m also assuming that you, dear reader, are a random person, and therefore most likely belong to the endless, but shallow, sea of short people.

Here’s the thing: since you are probably short you are likely to be unaware of how tall people suffer, so I’m going to tell you. For reference, I am a shade over six-two, which is tall, but not professional basketball player tall. This is still taller than more than nine-tenths of the American population, however.

Life as a tall man is not all bad. It’s true I’ve developed strong forearms from beating off adoring females who lust after my tallness, but there are many more misfortunes that outweigh the unending adulation of women. Showers for one.

Shower heads come to mid-chest on me. I’ve developed a permanent stoop from years of bending over to wash my hair—and then from scrunching down to see my reflection in the mirror, typically placed navel high, so that I can comb it.

The lamentations of the tall when it comes to airplane seats are too obvious to mention. As is our inability to fit into any bathtub or fully on any bed.

I once worked in a building that required, for security reasons, a peephole to be drilled into the door. I stood guard over two workers who dickered over where to place the pencil mark that would indicate where they were going to drill. Each in turn stepped up the door and put a dot in the spot where their eye met the door. The marks didn’t quite match but they soon settled on the difference.

Ultimately, the hole was about crotch high on me. To be fair, I was in Japan and the workers were Japanese, and therefore on the not tall side of the scale. Because I was in the military, I wasn’t entirely comfortable bending down to that degree1. This meant that I breached security each time I opened the door because I couldn’t see who was on the other side. Suspicious, is it not?

It was at this point that I began to believe that this discrepancy in height was not entirely genetic and that sinister motives may be behind the prejudices of the non-tall.

For example, I have to place my computer monitor on three reams of paper so that it approaches eye level, and I have to raise my chair to its maximum so that my knees aren’t in my chin, but when I do my legs won’t fit under the desk. No matter how I position myself I am in pain. I sit2 in a factory made cubicle-ette which, as far as I can tell, causes no difficulties for my more diminutive co-workers. This is more evidence of the extent of the conspiracy of the non-tall.

Shopping is suspiciously dreadful too. Short people can freely walk into any department store and grab something, anything, off the rack, while we tall men are stuck with places like Ed’s Big and Tall. These stores are fine if you have a waist of at least 46 inches and you have stumpy legs, but they are nearly useless otherwise.

Pants for the tall are a cruel joke. Even if they carry labels that promise lengths of 35 or more inches, we know that these labels are a lie. Yes, the legging material may stretch for yards and yards, but there is never enough space where it counts. These pants are called “short-rise” for obvious reasons. I asked a salesguy (a non-tall man, of course), do they make long-rise pants anymore? He didn’t stop laughing. Normally, I’d have my revenge by not buying anything from him, but I couldn’t buy anything from him in the first place. I could do nothing but fume.

I’m not sure how we, the tall, will be able to overcome these horrific adversities. In raw numbers we are but a small minority—a fairly imposing looking minority it’s true—but a minority just the same. Still, there is word that something can be done and I hear that we’re to discuss ideas at our next official Tall Man Meeting. Don’t bother trying to sneak in, though, because we take measurements at the door.

1If I would have been in the Navy, I would have been used to it, of course.
2This was true then; it no longer is. I do not have a desk now.
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